No browser AFAIK has the ability to patch a running process (it's very hard to do in general, but there are some ways to do it to a linux kernel for example). So you must restart to actually run the downloaded updates. Which means until you restart, you are running an unpatched browser which might have known exploits.
If each tab is a separate process, they could be upgraded one by one. You could even signal to each tab that it should open all links in a new process. Browsers are probably the app you could most easily transparently upgrade.
Not correct. Multiprocess browsers like Chrome don't actually run an entire browser in each process (that isn't realistically possible) because the individual tabs need to collaborate for the proper functioning of things like caches, cookies, etc.
If. If I can restart a web server without restarting memcache and have a new process handle new requests while the old process handles existing requests, it's clearly possible for a browser to change its rendering engine for new tabs.
On Ubuntu, Chrome and FF updates are pushed through the repos and are updated through apt-get / Update Manager. It's not annoying at all, and works like clockwork. Kudos to Chrome, FF and Ubuntu!
On Windows, Chrome does a good job auto update in the background. Firefox am not so sure but they too are working on some kind of auto update. Good for them, not being stubborn, and implementing a good feature that their rival has.
Good for Chrome that they aren't suing others trying to implement auto update. :-)
